Output Control by Linear Time-Varying Systems using Parametric Identification Methods

In this paper the problem of control for time-varying linear systems by the output (i.e. without measuring the vector of state variables or derivatives of the output signal) was considered. For the control design, the well-known online procedure for solving the Riccati matrix differential equation is chosen. This procedure involves the synthesis of linear static feedbacks on state variables in the case of known parameters of the plant. If state variables are not measured, then for the observer design using the matrix Riccati differential equation, using the dual scheme, which provides for the transposition of the state matrix and the replacement of the input matrix by the output matrix. It is well known that an observer of state variables built on the basis of a solution of the Riccati matrix differential equation ensures the exponential stability of a closed loop system in the case of uniform observability. Despite the fact that this type of observer can be classified as universal, its have a number of significant drawbacks. The main problem of such observers is the need for accurate knowledge of the parameters and the requirement for uniform observability, which in practice cannot always be realized. Thus, the problem of the new methods design for constructing observers of state variables of linear non-stationary systems is still relevant. Some time ago, a number of methods for the adaptive observers design of state variables for nonlinear systems were proposed. The main idea of the synthesis of observers was based on the transformation of the original dynamic system to a linear regression model containing unknown parameters, which in turn were functions of the initial conditions of the state variables of the control object. This approach in the English language literature is called PEBO. This paper, based on the PEBO method, proposes a new approach for the observers design of state for non-stationary systems. This approach provides the possibility of obtaining monotonic convergence estimates with transient time tuning.

Asymptotically tracking control for discrete time-varying link system to structural balance via determined external stimulations

This paper is concerned with the structural balance problem for complex dynamical network with the help of coupling effect related to the external stimulations. Consider a network with time-varying and value-weighted links, which can be regarded as a dynamic system. The link dynamic system is modeled as a Riccati matrix difference equation with the coupling matrix related to the external stimulations. By using the Kronecker product as an effective tool, a linear matrix inequality (LMI) approach is developed to derive a simple criterion for ensuring that the discrete link system asymptotically achieves structural balance, meanwhile, the external stimulations track a corresponding vector signal as well. Simulation examples are given to demonstrate the usefulness of the proposed control scheme in this paper.